Microwave studies of the Gaussian symplectic and the chiral ensembles

混沌系统谱的普适性，如邻近特征值的间距分布，与具有相应对称性的随机矩阵系综的谱的普适性一致。这种普遍性是Bohigas， Giannoni， Schmit的同时被证明猜想的本质。没有自旋1/2的时间反转对称系统用高斯正交系综（GOE）描述，自旋1/2的系统用辛正交系综（GSE）描述，自旋破碎的时间反转对称系统用酉系综（GUE）描述。GOE的实验实现数量很多，而GUE的实验实现数量很少。对于GSE，我们在本项目中实现了随机矩阵理论（RMT） 50年来的第一个实验实现，即在微波图中实现一个具有特殊对称性的网络，模拟自旋1/2系统。在这个项目的继续，我们计划研究GSE图的散射特性。除了本申请中描述的我们小组的第一个实验外，这是一个全新的研究领域。此外，在GOE和GUE中建立良好的RMT仍然需要在GSE的主要部分进行开发。对于具有粒子-反粒子对称性的系统，出现了三种新的随机矩阵系综，分别是手性GOE、GUE和GSE。在我们的第一个应用中，我们提出在由介电圆柱体建立的微波等效石墨烯中实现手性GOE。由于应用程序中描述的原因，我们决定改变为一个更简单的系统，它已经表现出手性对称，线性链。正在进行的实验表明，我们已经成功地实现了手性GOE。在延长期间，我们计划将研究扩展到手性GUE和手性GSE。该项目的主要目标是首次实验实现十个随机矩阵集合中的四个。通过外部驱动二极管与T结的组合，可以生成非平稳图形。利用GSE图中的周期时间依赖关系，我们计划实现自旋共振的微波等效。甚至一个等效的自旋弛豫也可以通过外加一个随机变化的时间依赖性来建立。这将为自旋弛豫理论的检验开辟一条新的途径。

The universal properties of the spectra of chaotic systems, e.g. the spacing distribution of neighboring eigenvalues, coincide with those of random matrix ensembles with corresponding symmetries. This universality is the essence of the meanwhile proven conjecture of Bohigas, Giannoni, Schmit. Systems with time-reversal symmetry (TRS) and no spin 1/2 are described by the Gaussian orthogonal ensemble (GOE), those with spin 1/2 by the symplectic (GSE), and those with broken TRS by the unitary (GUE) ensemble.There is an abundant number of experimental realizations for the GOE and a small number for the GUE. For the GSE the first experimental realization after 50 years of random matrix theory (RMT) had been achieved by us in the present project in a microwave graph, a network with peculiar symmetries mimicking a spin 1/2 system.In the continuation of this project we plan to study the scattering properties of GSE graphs. Apart from a first experiment in our group described in this application, this is a completely new field of research. Also RMT, well established for the GOE and the GUE, still has to be developed in mayor parts for the GSE.For systems with particle-antiparticle symmetries three new random matrix ensembles appear, the chiral GOE, GUE, GSE, respectively. In our first application we proposed to realize the chiral GOE in a microwave equivalent of graphene set up by dielectric cylinders. For reasons described in the application we decided to change to a much simpler system, which already exhibits chiral symmetry, the linear chain.The ongoing experiments already demonstrate that we had been successful in the realization of the chiral GOE. In the prolongation we plan to extend the studies to the chiral GUE and the chiral GSE. The main objective of this project including its prolongation is the first experimental realization of four of the ten random matrix ensembles.By means of a combination of an externally driven diode with a T junction non-stationary graphs may be generated. Using periodic time dependencies in a GSE graph we plan to realize a microwave equivalent of spin resonance. Even an equivalent of spin relaxation can be established by applying in addition a stochastically varying time-dependence. This would open a new access to the test of spin relaxation theories.